Chapter 11: Conic Sections
Conic sections — parabolas, ellipses, and hyperbolas — are the curves formed by slicing a cone at different angles. They appear in planetary orbits (ellipses), satellite dishes (parabolas), and cooling towers (hyperbolas). Each has a standard equation and key geometric features.
Textbook alignment
Sections
11.1Parabolas
A parabola is the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). The parameter p is the signed distance from vertex to focus. Completing the square converts general form to standard form, revealing vertex, focus, and directrix.
11.2Ellipses
An ellipse is the set of all points where the SUM of distances from two foci is constant (= 2a). It looks like a flattened circle. The longer axis is the major axis (length 2a); the shorter is the minor axis (length 2b). The relation c² = a² − b² connects the three key distances.
11.3Hyperbolas
A hyperbola is the set of all points where the DIFFERENCE of distances from two foci is constant (= 2a). It has two separate branches, each with a vertex, and approaches two asymptotes as it extends outward. Key formula: c² = a² + b² (PLUS, unlike the ellipse).
What's included — free
- ✓Visual concept explanations with diagrams for every section
- ✓Step-by-step worked examples you can study at your pace
- ✓Key vocabulary and memory aids for each topic
- ✓Printable worksheets generated for each section
Upgrade for unlimited practice, private tutoring, study planner, and exam mode. View plans